Dynamical error in nonlinear filtering

The authors describe the phenomenon of dynamical error, a source of error in parameter estimates of nonlinear models. They show that dynamical error is the result of complex dynamics of the nonlinear time series, such as limit cycles and chaos, permeating the estimation equations. The decay rate of dynamical error becomes an additional, often dominant, effect in the parameter convergence rate and in the selection of data set size. It is shown that new nonlinear adaptive filtering methods attenuate dynamical error more rapidly than batch methods. Therefore, as a practical matter, sample-by-sample methods are superior to batch methods when the underlying dynamics is nonlinear. Dynamical error is offered as a possible explanation for the difficulty in modeling certain nonlinear time series, particularly the Canadian lynx data. The authors´ results are illustrated by numerical examples drawn from the logistic map